The president mentions the possibility of a Camp David meeting with Hill leaders

Washington (CNN) -- President Barack Obama told GOP leaders behind closed doors Tuesday that he had failed to reach across party lines enough during his first two years in office, a senior administration official told CNN.

He promised to do a better job of bipartisan outreach in the days ahead, the official added.

"The president said he had to do better, and the president is ready to do his part," the official said.

Boehner, the top Republican in the House, is set to become speaker in January.

Boehner also said Obama told him that he "didn't spend enough time" working with the Republicans since taking office.

The president said after the meeting that he has invited Republican and Democratic congressional leaders to meet with him again several times in the future, including for a Camp David summit -- an idea considered by the administration for several weeks.